A cutting device for web materials is known from DE 36 08 111 C1, which demonstrates two cutter bars positioned over one another. The cutter bar is directly driven on each end by an electric motor. The cutter bars are connected mechanically on both sides by intermeshing gear pairs. The intermeshed gears possess spiral gearing. One gear of a gear pair is movable. The disadvantage is that the angular momentum of all moving components, such as electric motors, gear pairs and cutter bars, is not minimized. Only two driving motors are used for one cutter bar. These motors must deliver the entire driving power for the cutting device. In addition, the intermeshed gears must be unnecessarily strongly constructed, thereby providing a high angular momentum, because the lower cutter bar must be driven with the corresponding torque.